ImageCorrelate¶

Correlates an image with a kernel.

Correlation multiplies the kernel with the neighborhood in the same orientation, so filtering a single lit pixel replays the kernel backwards:

$ wo 'ImageData[ImageCorrelate[Image[{{0., 0., 1., 0., 0.}}], {{1, 10, 100}}]]'
{{0., 100., 10., 1., 0.}}

ImageConvolve reflects the kernel first, which is the one thing that tells the two apart — its impulse response is the kernel the right way round:

$ wo 'ImageData[ImageConvolve[Image[{{0., 0., 1., 0., 0.}}], {{1, 10, 100}}]]'
{{0., 1., 10., 100., 0.}}

The kernel entries are reflected however they are written, so a kernel of rationals behaves like any other:

$ wo 'Round[111 ImageData[ImageCorrelate[Image[{{0., 0., 1., 0., 0.}}], {{1, 10, 100}}/111]]]'
{{0, 100, 10, 1, 0}}

A kernel that is its own reflection makes them agree, so the usual GaussianMatrix / BoxMatrix / DiskMatrix kernels can be used with either:

$ wo 'ImageData[ImageCorrelate[Image[{{0., 1., 0.}}], GaussianMatrix[1]]] == ImageData[ImageConvolve[Image[{{0., 1., 0.}}], GaussianMatrix[1]]]'
True

The boundary is extended by repeating the edge pixels, and the image keeps its dimensions and channel count:

$ wo 'ImageDimensions[ImageCorrelate[Image[{{{1., 0., 0.}, {0., 1., 0.}}}], BoxMatrix[1]/9]]'
{2, 1}

A first argument that is not an image is reported:

$ wo 'ImageCorrelate[5, {{1}}]'

ImageCorrelate::imginv: Expecting an image or graphics instead of 5.
ImageCorrelate[5, {{1}}]